Below is a look at how Apple's market capitalization grew from $4.8 billion back in December 2000 to $417 billion today. Since December 2010, Apple's valuation has gone up $183 billion or nearly 79 percent.Apple's title of biggest company in the world is secured by a $2 billion difference with the second-largest company in the S&P 500, Exxon Mobil. Will Apple remain on top?